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Question

$m,x$

$m,{1 \over x}$

$m,{1 \over {{x^2}}}$

$m,{x^2}$

Solution

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Step-by-Step Explanation Step 1: Identify the Quantities Involved The question involves determining the correct dimensional form of two physical quantities that appear to be the amplitude and wave number (or similar parameters in a wave-related context). The options include possible dimensions like $m$, $1/x$, $1/x^2$, or $x^2$. Based on wave concepts, amplitude typically has the dimension of length, while the wave number has the dimension of inverse length. Step 2: Determine the Dimension of Amplitude Amplitude (often denoted by $A$) is a measure of displacement. Displacement is measured in meters ($m$) in SI units. Therefore, the dimension of amplitude is: $$ [A] = M^0L^1T^0 \quad \text{(i.e., meters)} $$ Step 3: Determine the Dimension of Wave Number The wave number (often denoted by $k$) is defined as $k = \frac{2\pi}{\lambda}$, where $\lambda$ is the wavelength (in meters). Hence, its dimension is the reciprocal of length: $$ [k] = \frac{1}{L} $$ So, it is measured in inverse meters, which corresponds to $1/x$ in the given options. Step 4: Match with the Given Options The correct pairing that matches one quantity with the dimension of length ($m$) and the other with the dimension of inverse length ($1/x$) is: $$ m, \frac{1}{x} $$ Step 5: Final Answer Verification This matches Option 2 in the given choices. The solution image provided illustrates a dimensional analysis argument leading to these conclusions.

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Biology Subject Chemistry Subject Mathematics Subject Physics Subject Subjects Subject

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Parent Quiz 751902

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